Calvo vs Mankiw/Reis, and IT vs PLPT/NGDPLPT

An economy is humming along very nicely in full long run equilibrium. All real variables are at their natural rates. Actual and expected inflation are both equal to the 2% inflation target. As the years go by, the price level goes: 90, 92, 94, 96, 98, and everybody expects it to continue 100, 102, 104, forever and ever.

Then a negative Aggregate Demand shock hits, and the central bank is slow to respond. Instead of going to 100, as everyone had expected, the price level in year 0 is 99. What else happens?

There's a recession. Real output and employment fall below their natural rates, and unemployment rises above its natural rate. But the story doesn't end there.

1. Now suppose that the central bank wakes up, announces that it will make sure the price level rises at 2% per year from now on, and everybody fully expects the central bank will do what it says, and the price level does in fact go: 99, 101, 103, 105, etc.

Question 1: in year 1, when the price level is 101, and the actual and and expected and target rates of inflation are all equal, will this economy still be in recession, or will it have completely recovered to the natural rates of output, employment, and unemployment?

2. Now suppose instead that the central bank wakes up, announces that the price level will rise by 3% in year 1, and 2% thereafter, and everyone fully expects the central bank to do what it says, and the price level does in fact go: 99, 102, 104, 106, etc.

Question 2: in year 1, when the price level is 102, and the actual and expected
and target rates of inflation are all equal, will this economy still be
in recession, or will it have completely recovered to the natural rates
of output, employment, and unemployment?

Question 3 (just for clarification): Are you saying that the levels of output, employment, and unemployment, will be the same in year 1 in both questions 1 and 2, even though the price level is 101 in question 1 and 102 in question 2?

The Calvo Phillips Curve, which is the theory of price adjustment most commonly used in New Keynesian macroeconomic models, basically answers "yes" to all three questions.

(I stuck in that weasel-word "basically" for two reasons: first, the variance of prices, output and employment across individual firms will be different in the Calvo model between 1 and 2, and this variance might affect aggregate output and employment, though this effect is usually ignored; second, because the recession in year 0 might have hysterisis affects, and this might affect the short run natural rates, but this still shouldn't prevent the answer to question 3 being "yes", because it would affect 1 and 2 equally.)

I think I would answer the three questions: 1. no; 2. probably (except for hysterisis); 3. no.

We can restate the question this way: are those recessions that are caused by drops in Aggregate Demand only (no "supply shocks") associated with: the inflation rate being below the previous trend path; or the price level being below the previous trend path? What belongs on the vertical axis of the Short Run Aggregate Supply/Short Run Phillips Curve: the inflation rate; or the price level?

The answer really matters for monetary policy. If you answer "yes" to all three questions, then there is nothing to choose (in this particular case) between Inflation Targeting and Price Level Path (or NGDP Level Path) Targeting. If you answer "no", "yes", "no" that is a very strong argument for PLPT (or NGDPLPT) over IT. And it's an argument that has nothing to do with: Zero Lower Bounds; automatic stabilisers for AD; supply shocks; risk-sharing between debtors and creditors.

I think this argument for PLPT (or NGDPLPT) is implicit in what Scott Sumner says, but I don't remember him laying it out explicitly. I'm not sure whether other supporters of NGDPLPT or PLPT, across the whole monetarist-keynesian spectrum, would or would not agree with with this particular argument.

Why do I answer those three questions the way I do?

Well, mostly it's the data. It must be the data, because I didn't use to think like this. If you had told me, back in 2009, that the inflation rate would quickly return to target (or to its previous trend in countries without an explicit target) I think I would have said "Right, no worries then, because inflation lags output and employment, so if inflation returns quickly to target there must be a very quick V-shaped recovery after a very short recession." I might have made a few caveats about hysterisis, I suppose.

The data don't tell a story that is anywhere near as clean as I would like, and if the SRAS/SRPC is fairly flat (which it seems to be), and if there are supply shocks (which there may be), it will be very hard to tell the two stories apart empirically. But I think it is a little easier to force the data to fit my story than to force the data to fit the Calvo Phillips Curve story.

Take Canada for example. Very crudely, inflation fell below the 2% target in early 2009, and returned to target by late 2010, but the real economy (unemployment for example) seemed to take a couple more years to recover (you could argue it has still not recovered fully). Here are the price data. What do you see? Remember there is total CPI and 3 different measures of core, and we could look at monthly as well as annual inflation rates. Note that the price level (both total and core) seems to still be a little below the pre-recession trend.

So much for the data. What about the theory?

Maybe something like Mankiw and Reis? The basic idea is that people just don't listen to the news very often, and keep on raising their prices at 2% per year regardless of what is happening around them, until they do eventually pay attention. It sounds daft, but it does seem to fit the facts.

Maybe some sort of convention in a model of multiple equilibria? Most people try to follow the convention, as long as they expect most other people will follow the convention. And if the convention is to raise prices at 2% per year, most people keep on raising prices by 2% per year.

So when AD fell only a few people cut their prices, so there was a recession. The recession then continues, with a slow recovery. Every year a few people listen to the news, or break convention, and raise their prices by less than 2%. But a few others, who had originally cut their prices when the recession hit, now raise their prices by more than 2% because the economy is slowly recovering so they don't want their relative prices to be quite so low as before. So the average inflation rate is 2%, even though the economy is still in recession and in a slow recovery

Any other theory?

We really do not know very much about the Short Run Aggregate Supply Curve/Short Run Phillips Curve. And yet it's really important. If something like the Mankiw/Reis model is roughly right, even if it's right for the wrong reasons, Inflation Targeting is bad policy, and something like Price Level Path Targeting or NGDP Level Path targeting would be much better policy. Quite apart from any other reasons for preferring some sort of level path target.

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"Question 1: in year 1, when the price level is 101, and the actual and and expected and target rates of inflation are all equal, will this economy still be in recession, or will it have completely recovered to the natural rates of output, employment, and unemployment?"

Do such natural rates exist? You mention multiple equilibria. Why shouldn't each equilibrium have its characteristic rates, none more "natural" than the others?

Then a negative Aggregate Demand shock hits, and the central bank is slow to respond. Instead of going to 100, as everyone had expected, the price level in year 0 is 99. What else happens?

There's a recession. Real output and employment fall below their natural rates, and unemployment rises above its natural rate. But the story doesn't end there.

The way you're saying it sounds as though the recession is a consequence of the price change. If the price of goods was unexpectedly low wouldn't people be even more eager than usual to exchange goods for money? And wouldn't the worst case be a negative demand shock that doesn't show up in prices at all?

You can of course imagine a world in which all precises were fixed by statute, and such a world could still have recessions (e.g. the babysitter co-op).

In the real world prices are somewhat flexible, and we see recessions associated with lower inflation (and occasionally outright deflation), but it seems as much a game of pushing the natural price level ('natural' in the sense of natural interest rates) to the actual price level as of pushing the actual price level to trend.

Of course, you can't actually see the natural price level (which is presumably a function of the monetary base, expected inflation, etc.) so you can only tell if you're their yet by looking at output. You don't know exactly what unemployment rate constitutes full employment, either, so you probably want to look for a way to make sure you keep output up but don't create runaway inflation in response to adverse supply shocks. If only there were a target that could handle both at the same time...

Maybe some sort of convention in a model of multiple equilibria? Most people try to follow the convention, as long as they expect most other people will follow the convention. And if the convention is to raise prices at 2% per year, most people keep on raising prices by 2% per year.

Imagine you are flying an airplane. You are planning to fly a particular route from takeoff to landing. You know that if you are on your route, the numbers on your altimeter will follow a particular path through time. So you "target the path" of altimeter measurements. You don't do this because your altimeter has any influence on what you care about (if you manually adjusted it to show the right time path, that wouldn't help), but because the thing you have to do to get the altimeter back on the path also gets your airplane back on its route.

Now, unlike your altimeter the actual observed price level does have some effect on the macroeconomy, but it may have much less than a lot of models seem to imply.

First this is a very good post. It turns attention to something I perceive as one of the most important questions for Market Monetarists (and Keynesians) out there: how come we did not not recover from the demand shock already? The preferred story of many economists is that it is because we may have supply side problems.

In this article: http://uneasymoney.com/2012/07/11/george-selgin-asks-a-question/ David Glasner has a neat proposal: it can be caused by divergent expectations. This actually seems to agree not only with this article of yours, but also with your thoughts about different inflation measures or different measures of interest rates etc. Maybe people are not "daft" but they use different information to make their plans. If the inflation in your basket of goods is different from the inflation of your basket of goods, it is easy to explain that our inflation expectations will diverge.

But to be honest, I do not know what to make out of this. There seems to be something missing here.

It depends on the model. They do in some models, and don't in others. Which of those two classes of models has one model that is roughly right? Dunno.

"You mention multiple equilibria. Why shouldn't each equilibrium have its characteristic rates, none more "natural" than the others?"

That's a possibility.

In this post my (imaginary) audience was a New Keynesian economist, and it was easier to talk to him using the natural rate concept.

Alex: "The way you're saying it sounds as though the recession is a consequence of the price change."

I didn't mean to make it sound like that. A little later I carefully say that the price change is "associated with" the recession (or vice versa). The way I see it, the leftward shift in AD is what causes both the drop in Y and the drop on P. If the SRAS/SRPC curve were horizontal, we would still get the recession, but no price change.

I'm really talking about price change (or inflation change) as a possible *symptom* and asking whether someone who didn't know whether an economy is in recession should use low price level or low inflation (relative to trend) as a symptom of recession. "Is it the number of spots, or the rate of change of the number of spots, that tells the doctor whether the patient still has the measles, or has recovered?"

Ah! You use the altimeter analogy. I use measles.

rsj: "Is there a reference?"

I don't really have one. It was more of a vague thought. I sort of sketch a theory in this old post. Maybe something vaguely like my old paper.

To me, Goodhart's law applies directly to interest rate targeting. If people are short on money, they plausibly sell assets for money, asset prices fall, and the interest rate rises. The central bank, seeing that increase in the interest rate, can expand the quantity of money (by purchasing assets,) this reverses the decrease in bond prices, and the increase in interest rates. The monetary disequilibrium is corrected.

Of course, this requires that the central bank have some notion of the appropriate level of interest rates--allowing some changes in interest rates and not others. Goodwin's law is that before long, the market changes in interest rates are driven by what market participants think the central bank believes are appropriate. Whether it likes it or not, the central bank is setting these interest rates at the level it likes.

Apply this to inflation targeting. If the central bank thinks it is looking at changes in the inflation rate to judge whether monetary policy is appropriate (which to me, is whether there is monetary disequilibrium,) then it will soon find that those actually setting prices of goods and services will be setting prices not to clear markets, but rather according to what they think the central bank wants.

If they think the central bank wants prices to rise 2% from wherever they are now, then that is what they will do.

Now, if all we care about is targeting inflation, then this is great. Just like if all we care about is keeping interest rates at a target level, Goodharts's law shows how a central bank can achieve this very effectively. But if we want to use changes in inflation to judge whether real expenditure is matching productive capacity, or whether or not there is an output gap, then Goodhart's law is a problem.

The more credible the central bank, the greater the problem with Goodhart's law.

So, rather than waiting for an output gap to slow inflation, and then gradually lower nominal interest rates so that the output gap closes and inflation returns to target, it is necessary to watch the output gap and adjust monetary policy to close the output gap.

Interestingly, with interest rate targeting, then it is important that the inflation target be credible. If slow growth in spending leads to lower inflation, then this tends to raise real interest rates, at least partly offsetting any decrease in nominal interest rates understaken by the central bank. But, if those setting the prices of goods and services pay attention to the central bank's target, and that target is credible, then this interferes with the ability of goods prices to reflect an output gap. A bit like catch 22.

Does that question mean (a) "Aggregate demand has returned to its pre-crash level, so why has unemployment not returned to its pre-crash level?" or (b) "Why has aggregate demand not returned to its pre-crash level?" ?

The answer to (a) is pretty simple: aggregate demand has not returned to its pre-crash level. Supply-side explanations are largely unnecessary, since it's not surprising to have a "jobless recovery" if there's no recovery.

AD falls. How do businesses respond? If the AD is caused by people being unemployed then the market shrinks. No reason to change price. It is not intuitive that lowering prices will gain market share without significant pain elsewhere, remember everyone is trying to save as much as possible. But there is a real reason to reduce overhead costs to become profitable (do you really need a better example of this then the current stock market?).

In this case if you raise inflation expectations you will raise prices but not effect unemployment. With the current AD problem low interest rates negatively effect savings and income. Higher interest rates will effect savings and prices, the effect on savings is the interest rate not he desire to save less. Neither will greatly effect income or unemployment.

The problem is demand, the only way to effect this problem is a direct injections through fiscal policies (lower taxes and/or more spending). Currently there is enough fiscal policy to create the current economic environment. As the policies change so will the economy. Is Japan not a good enough example?

"As the policies change so will the economy. Is Japan not a good enough example?"

Nope, because fiscal deficits and unemployment were positively correlated in Japan: unemployment didn't hit 5% until after the budget deficit passed 6%. Correlation does not equal causation, but inverse correlation implies non-causation. Japan is surely an example of how you can have all the debt-financed fiscal stimulus you want, but if the central bank is targeting price stability it's at best a waste of time-

http://research.stlouisfed.org/fred2/graph/?id=GGNLBAJPA188N#

Put another way, the fiscal multiplier is at best zero in a modern economy i.e. one with an independent central bank. Japan is a great example of this.

Fed policy is endogenous: the Fed sets a 2% goal, with no make-up. expectations matter, Fed policy - implicit or not - gets baked into business plans, because when one is doing a budget, one just knows the central bank will shoot for 2% inflation.

Very interesting, Nick. This got me wondering about the "price variance term" in the Calvo model that you mentioned. It is usually ignored (because it is not first order) but how large an effect could it have? Is second order enough to be important? A few people have started solving Calvo models numerically with non linear solutions, so the answer might be out there. If it is important, then even under Calvo pricing price level targeting might be better.

Maybe inflation is overstated in recessions. Suppose that instead of cutting prices on existing products, firms prefer to introduce new lower cost products. This is effectively a price cut, but wouldn't register as a price cut in an inflation index (right?)

I downloaded and started toreadn mankiw ries
and i'm not ashamed to admit I didn't quite grasp equation 1, which is like preK economics math
However, the discussion following eqn 1 (middle of page 5 in the pdf) sounds just wrong.

I mean, have any of you people ever asked how mmuch paperwork is invovled in changing prices, and how irratated distributors get, and....

Maybe it is all there, and I don't get it, but it sounds like autistic rational economics, ie autism is something where you have rigid stereotyped behavour (use of math) that doesn't capture the sublty of how people express themeslves (the real world of people and firms)
so autistic economics is rigid stereotyped behavour where you use math, even tho it is in appropriate and doesn't capture complexitys that really exist

Bill: very interesting comment. Inflation targeting sows the seeds of its own destruction, by destroying the signal in inflation, effectively making the Phillips Curve too flat. (This is maybe partly related to my own old "Milton Friedman's Thermostat" stuff.) Have you done a post on this?

W. Peden: think of it this way: if you thought that inflation being higher or lower than trend were a symptom of recessions, then if inflation were back on trend, it would make sense to ask why we see inflation back on trend and what appears to be a continuing recession.

Dan: "It is not intuitive that lowering prices will gain market share without significant pain elsewhere,..."

It is normally intuitive that demand curves slope down. If one firm cuts its price below competitors' prices, it will increase sales. If this weren't true the firm would always have an incentive to raise price, and all prices would be infinite.

dwb: Not sure if I understand that theory. It sounds like a bit of a mix of the theories Bill sketched and I sketched.

Brit: "If it is important, then even under Calvo pricing price level targeting might be better."

I don't think that follows, but I'm not 100% sure. The key to Calvo (the assumption that makes the model analytically tractable) is that the probability of changing price is independent of when you last changed it. If you want to minimise the variance of prices across firms, following a shock that caused them to disperse, the best policy is (I think) to keep the price level constant at whatever level it is at now. So the price level would follow a random walk. Which is inflation targeting.

Max: "This is effectively a price cut, but wouldn't register as a price cut in an inflation index (right?)"

Well, Stats Canada does *try* to hold quality constant when it measures inflation. There was a recent paper related to this, that someone (Menzie Chinn?) blogged about just a couple of days ago.

ezra: "I mean, have any of you people ever asked how mmuch paperwork is invovled in changing prices, and how irratated distributors get, and...."

Yep. And those sorts of costs could explain why firms don't change prices every day, or why prices are sticky. But they can't (so easily) explain why firms keep on raising prices by the same 2% every year.

How does inflation data compare to aggregate stock to sales ratio data?

Most of the time hagan das ice cream is $8. Then sometimes it's $5 until the freezer is emptied then the freezer is restocked and it goes back to $8.

Falling demand would result in rising stock to sales ratios. Reduced demand results in fewer orders which means scaled back production. Falling production means higher and rising marginal costs (in the real world) the further from full capacity utilization you get; all else equal. Same goes for supermarket purchase contracts of whatever. I think your idea about the 2% price increase is correct it's just automatic convention and is a cost that must be accounted for like dwb said. My guess is that it is the build up of inventory or the run down in inventory that determines the direction and magnitude of price changes. It is true that anyone would be willing to supply more at higher prices; they would likely also be willing to supply more at lower prices up their particular capacity constraints. While it is also true that most people would be willing to buy more at lower prices; they would likely also be willing to buy more as prices are rising (think houses and things I plan on selling). I would argue, probably incorrectly, that inventories and the desire to maintain margins are important variables affecting strength or ability to negotiate price changes for production and consumption goods and would help to explain what I think is the original theme of the post which is about why we have inflation in a recession?

Also, I'm not sure how cutting prices prevents recessions if someone could explain it to me I would be appreciative. Does that depend on rising marginal costs of production? Or is it the idea that everyone needs to cut prices all the way down the chain since money is neutral then everything is the same just that we changed the unit of measurement?

I apologize if I missed the point and sullied your comment section with nonsense.

> But I think it is a little easier to force the data to fit my story than to force the data to fit the Calvo Phillips Curve story.

Nick, from your references to the data, it seems that:

(1) inflation rate targeting was not enough (since output is still low)

(2) level target would be *better* since it would have led to *more* monetary stimulus, and we think that *more* monetary stimulus would have been better

(3) we don't know whether level targeting is a *sufficient* solution... it is possible that output would be low even if this policy were adopted. For example, level targeting puts us on a linear path. Maybe the required path is quite complicated, like a log-linear curve. OR, maybe we want to apply min-level targeting to multiple financial measures, like price level, NGDP level, wage level, etc.

Question 1: in year 1, when the price level is 101, and the actual and and expected and target rates of inflation are all equal, will this economy still be in recession, or will it have completely recovered to the natural rates of output, employment, and unemployment?

Isn't this the same as asking: Suppose P is true. Is Q true or is Q false?

And isn't "yes" always a logical answer to this question, no matter what you believe about economics?

Nick, Sorry for the slow response, but I'm still in China. I was very interested in your paragraph about what you would have thought in 2009, and what actually happened. In 2009 I would have thought that the "price" that mattered was hourly nominal wages. I would have thought that wage targeting (even rate targeting) would have prevented a severe and long lasting recession in the US. But unlike price inflation, wage inflation fell a couple points in the US, and stayed at a lower level (from just under 4% to just under 2%, if my memory is correct.)

In that case wage inflation rate targeting might have done just as well as level targeting of wages. Or at least the stylized facts don't rule out that possibility.

I'd still favor level targeting for other reasons. But perhaps the problem isn't the "rate" part of inflation targeting, but that we chose the wrong index. We needed to target the inflation rate of labor inputs, not the inflation rate of goods and services output. Any money policy robust enough to generate 4% wage increases in the US, would have been stimulative enough to keep unemployment from staying up near 8% to 10%.

Scott: I'm still thinking this through. See my more recent post on the same topic. I think wages (or at least, many wages), are like a supertanker. You target the supertankers. Don't make them try to change either position or direction.

mobile: Yep, strictly, my question was multiple choice, with two answers A or B, rather than a yes/no.

Patrick: not a stupid question. And there is probably some truth to it. If monetary policy has been aimed at making it optimal to increase prices by 2% a year, then many firms will perhaps just start following a rule of thumb where they keep raising prices at 2% per year regardless of circumstances. But economists aren't generally happy to assume that people will keep on following a rule of thumb when circumstances change, especially when doing so would seem to lead to big obvious mistakes and losses. And we do observe people seeming to follow rules of thumb, but we also do observe those rules of thumb changing over time (firms used to raise prices by a lot more than 2% per year). So it may be part of the story, but not the whole story.

marris: yes, yes, and maybe/dunno/but we need to keep it simple and good rather than try for complicated perfection.

Leon: yep. For Canada it really did use to look like price level path targeting, rather than IT. But over the last few years it looks a little more like IT. And Canada did have a milder recession than most. And there are supply shocks too, which muddy the data.

"Also, I'm not sure how cutting prices prevents recessions if someone could explain it to me I would be appreciative. Does that depend on rising marginal costs of production? Or is it the idea that everyone needs to cut prices all the way down the chain since money is neutral then everything is the same just that we changed the unit of measurement?"

Whether or not cutting prices quickly can prevent a fall in AD causing a recession depends on the shape of the AD curve, which in turn depends on what the central bank is holding constant. If the central bank holds a rate of interest constant, the AD curve is vertical, and a cut in P won't help. If the CB is holding constant some nominal variable, then the AD curve slopes down, and a cut in P will help. But fully exploring that would take too long for a comment. And this post is about the SRAS/SRPC curve, not the slope of the AD curve. I am looking at falling prices vs falling inflation as a *symptom* of recession, setting aside the question of whether it could *cure* the recession, given the AD curve.